Hamilton's principle of stationary action is one of the most fundamental results of classical mechanics and is commonly used to derive equations of motion for a variety of systems. The forces and interactions that govern the dynamical evolution of the system are easily determined through Hamilton's principle in a formulaic and elegant manner. Hamilton's principle [1]} states that: The motion of the system between two fixed points from \(t_0\)  to \(t_f\)  is such that the action integral has a stationary value for the actual path of the motion. To derive the Euler-Lagrange equations via Hamilton's principle, we start by defining the configuration space, tangent space and path space.
